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Living systems continuously transform matter and energy through the chemical processes that constitute their metabolism. The overall metabolic rate of an organism correlates positively with its body mass, however both the exact scaling…
The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e. proliferation or differentiation)…
This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…
The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
Living systems self-organize in ways that conventional physical frameworks-based on forces, energies, and continuous fields-cannot fully capture. Processes like gene regulation and cellular decision-making involve rule-based logic and…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
We perform numerical simulations of isolated, partially active polymers, driven out-of-equilibrium by a fraction of their monomers. We show that, if the active beads are all gathered in a contiguous block, the position of the section along…
Cells contain elaborate and interconnected networks of protein polymers which make up the cytoskeleton. The cytoskeleton governs the internal positioning and movement of vesicles and organelles, and controls dynamic changes in cell…
Communication between cells is realized by exchange of biochemical substances. Due to internal organization of living systems and variability of external parameters, the exchange is heavily influenced by perturbations of various parameters…